Biomedical Engineering Reference
In-Depth Information
(a)
(b) (c)
(d)
(e) (f )
Figure 6.20: (a) A brain PET image from a 3D data set with high level of noise.
(b)-(f) Modulus of wavelet coefficients at expansion scale 1 to 5.
beneficially assist such wavelet expansion based on first derivative of spline
wavelets. Without seeking external a priori information, it was observed that
wavelet modulus from the next higher wavelet level can serve as a good edge
estimation. An edge indication map with values between 0 and 1 (analogous to
the probability that a pixel is located on an edge) was therefore constructed
by normalizing the modulus of this subband. A pixel-wise multiplication of the
edge indication map and the first level wavelet modulus can identify the location
of wavelet coefficients that are more likely to belong to a true anatomical edge
and should be preserved, as well as the locations of the wavelet coefficients
that are unlikely to be related to real edge signal and that should be attenuated.
This approach is referred to as cross-scale regularization. A comparison be-
tween traditional wavelet shrinkage and cross-scale regularization for recover-
ing useful signals from the most detailed level of wavelet modulus is provided in
Fig. 6.21.
A cross-scale regularization process does not introduce any additional pa-
rameter avoiding extra complexity for algorithm optimization and automation.
We point out that an improved edge indication prior can be built upon a modified
wavelet modulus in the next spatial-frequency scale processed using traditional
thresholding and enhancement operator.
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